Properties

Label 4021.2.a
Level 4021
Weight 2
Character orbit a
Rep. character \(\chi_{4021}(1,\cdot)\)
Character field \(\Q\)
Dimension 334
Newforms 3
Sturm bound 670
Trace bound 1

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Defining parameters

Level: \( N \) = \( 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4021.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(670\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4021))\).

Total New Old
Modular forms 335 335 0
Cusp forms 334 334 0
Eisenstein series 1 1 0

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators.

\(4021\)Dim.
\(+\)\(152\)
\(-\)\(182\)

Trace form

\(334q \) \(\mathstrut +\mathstrut 330q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 334q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(334q \) \(\mathstrut +\mathstrut 330q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 334q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 10q^{11} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 326q^{16} \) \(\mathstrut -\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 8q^{18} \) \(\mathstrut -\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 2q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut +\mathstrut 16q^{22} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut +\mathstrut 2q^{24} \) \(\mathstrut +\mathstrut 336q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 6q^{27} \) \(\mathstrut -\mathstrut 4q^{28} \) \(\mathstrut -\mathstrut 4q^{29} \) \(\mathstrut +\mathstrut 2q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 14q^{35} \) \(\mathstrut +\mathstrut 354q^{36} \) \(\mathstrut -\mathstrut 4q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 50q^{40} \) \(\mathstrut +\mathstrut 8q^{41} \) \(\mathstrut +\mathstrut 28q^{42} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 46q^{44} \) \(\mathstrut -\mathstrut 4q^{45} \) \(\mathstrut -\mathstrut 28q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 328q^{49} \) \(\mathstrut +\mathstrut 6q^{50} \) \(\mathstrut +\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 42q^{52} \) \(\mathstrut -\mathstrut 8q^{53} \) \(\mathstrut +\mathstrut 14q^{54} \) \(\mathstrut -\mathstrut 6q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut +\mathstrut 40q^{59} \) \(\mathstrut -\mathstrut 64q^{60} \) \(\mathstrut -\mathstrut 42q^{61} \) \(\mathstrut -\mathstrut 16q^{62} \) \(\mathstrut -\mathstrut 38q^{63} \) \(\mathstrut +\mathstrut 314q^{64} \) \(\mathstrut -\mathstrut 34q^{65} \) \(\mathstrut -\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 26q^{68} \) \(\mathstrut -\mathstrut 32q^{69} \) \(\mathstrut -\mathstrut 14q^{70} \) \(\mathstrut -\mathstrut 8q^{71} \) \(\mathstrut -\mathstrut 2q^{72} \) \(\mathstrut -\mathstrut 22q^{74} \) \(\mathstrut -\mathstrut 42q^{75} \) \(\mathstrut -\mathstrut 60q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 52q^{78} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut +\mathstrut 310q^{81} \) \(\mathstrut -\mathstrut 36q^{82} \) \(\mathstrut +\mathstrut 18q^{83} \) \(\mathstrut -\mathstrut 136q^{84} \) \(\mathstrut +\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 34q^{86} \) \(\mathstrut -\mathstrut 24q^{87} \) \(\mathstrut -\mathstrut 10q^{88} \) \(\mathstrut -\mathstrut 38q^{89} \) \(\mathstrut -\mathstrut 130q^{90} \) \(\mathstrut -\mathstrut 16q^{91} \) \(\mathstrut -\mathstrut 36q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 14q^{96} \) \(\mathstrut +\mathstrut 6q^{97} \) \(\mathstrut -\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 100q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4021))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 4021
4021.2.a.a \(1\) \(32.108\) \(\Q\) None \(-2\) \(1\) \(3\) \(4\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}+3q^{5}-2q^{6}+\cdots\)
4021.2.a.b \(151\) \(32.108\) None \(-16\) \(-29\) \(-27\) \(-18\) \(+\)
4021.2.a.c \(182\) \(32.108\) None \(18\) \(28\) \(22\) \(14\) \(-\)